The discovery of Novoselov et al. (2004) of a simple method to transfer
a single atomic layer of carbon from the c-face of graphite to a substrate suitable
for the measurement of its electrical and optical properties has led to a renewed interest
in what was considered to be before that time a prototypical, yet theoretical,
two-dimensional system. Indeed, recent theoretical studies of graphene reveal that
the linear electronic band dispersion near the Brillouin zone corners gives rise to
electrons and holes that propagate as if they were massless fermions and anomalous
quantum transport was experimentally observed. Recent calculations and experimental
determination of the optical phonons of graphene reveal Kohn anomalies
at high-symmetry points in the Brillouin zone. They also show that the Born–
Oppenheimer principle breaks down for doped graphene. Since a carbon nanotube
can be viewed as a rolled-up sheet of graphene, these recent theoretical and experimental
results on graphene should be important to researchers working on carbon
nanotubes. The goal of this contribution is to review the exciting news about the
electronic and phonon states of graphene and to suggest how these discoveries help
understand the properties of carbon nanotubes.